Capital recovery factor

A capital recovery factor is the ratio of a constant annuity to the present value of receiving that annuity for a given length of time. Using an interest rate i, the capital recovery factor is:

where is the number of annuities received.[1]

This is related to the annuity formula, which gives the present value in terms of the annuity, the interest rate, and the number of annuities.

If , the reduces to . Also, as , the .

Example

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With an interest rate of i = 10%, and n = 10 years, the CRF = 0.163. This means that a loan of $1,000 at 10% interest will be paid back with 10 annual payments of $163.[2]

Another reading that can be obtained is that the net present value of 10 annual payments of $163 at 10% discount rate is $1,000.[2]

References

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  1. ^ Calculator by Jenkins at University of California Archived July 8, 2006, at the Wayback Machine
  2. ^ a b "Capital Recovery Factor". www.homerenergy.com. Retrieved 2019-03-18.
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Wolfram|Alpha Capital Recovery Factor Calculator